6Li spin-alignment echo (SAE) nuclear-magnetic-resonance (NMR) spectroscopy is used to monitor single-particle two-time correlation functions in LiAlSi2O6 glass. The method, here applied in the temperature range from 300 to 400 K, is sensitive to ultraslow Li hopping processes with rates (1/τSAE) down to 10 jumps/s. The use of a sample with natural 6Li abundance allowed the measurement of pure NMR spin-alignment echoes which are damped with increasing mixing time exclusively by slow Li jumps, i.e., free of influences arising from, e.g., interfering spin-diffusion effects. The considerably stretched correlation functions reveal the presence of a broad distribution of jump rates. The results are comprehensively compared with those recently obtained from both 7Li SAE and 7Li spin-lattice relaxation NMR as well as from dc conductivity measurements. Interestingly, the activation energy of the latter, which are sensitive to long-range Li transport parameters, is in good agreement with that microscopically probed by 6Li SAE NMR, here. © 2008 The American Physical Society.